An efficient algorithm for frame-based signal processing

In this paper we study the optimal sparse approximation to signals in the scenario of denoising using frames. We show that it produces the best denoising performance in terms of SNR values. Then we assume that the frame is the union of a collection of orthogonal bases and formulate a general modeling framework that unifies and extends several state-of-the-art statistical signal processing methodologies, including translation-invariant wavelet methods. At the heart of this framework is a novel signal model that combines/fuses several basis systems into a single observed signal representation through a pixel-wise model selection criterion, and derives a MAP estimator for each pixel. This framework overcomes several limitations of existing basis selection methods.